These questions really took me back to college math classes… Glad I still remembered how to do them

-What is the limit of (Cos(x)-1)/x^2 as x approaches 0?

-Alice and Bob choose an integer each in the range of [1, 10]. All choices are equally likely. What is the probability that neither of the chosen numbers will be the square of the other?

-If the probability of a random variable X with space R_x = {1, 2, 3, …, 12} is given by f(x) = k*(2x-1), then, what is the value of the constant k?

-f(x) = integral of (1+t^4) dt from 3 to x. Find f^(-1)’(0), the derivative of the inverse of f, evaluated at 0.

-Which of the following vectors does NOT belong to the subspace spanned by -2i+3j+k and I+j+2k?